document.write( "Question 488247: If we choose x from the set of values bigger than 0, is y = x² a function of x? explain
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\n" ); document.write( "If we choose y from the set of values bigger than 0, is y = x² a function of y? explain
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Algebra.Com's Answer #333328 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
y = x^2 makes y a function of x.
\n" ); document.write( "the independent variable is x and the dependent variable is y.
\n" ); document.write( "x^2 = y makes x^2 a function of y.
\n" ); document.write( "the independent variable is y and the dependent variable is x^2.
\n" ); document.write( "if we let z = x^2, then:
\n" ); document.write( "x^2 = y becomes z = y
\n" ); document.write( "z is considered a function of y because it depends on the value of y.
\n" ); document.write( "you would solve this like you would solve any equation.
\n" ); document.write( "if y = 5, then z = 5
\n" ); document.write( "since z = x^2, this means that x^2 = 5.
\n" ); document.write( "suppose you had:
\n" ); document.write( "x^2 = y-3
\n" ); document.write( "x^2 is still a function of y because it depends on the value of y.
\n" ); document.write( "if y = 5, x^2 = y - 3 = 5 - 3 = 2
\n" ); document.write( "you get x^2 = 2 when y = 5
\n" ); document.write( "i believe this to be true, but i won't swear to it.
\n" ); document.write( "there may be some rule that says you can't do this, but i haven't seen it.
\n" ); document.write( "in practice, you can set anything equal to anything else.
\n" ); document.write( "the dependent variable is a function of the independent variable.
\n" ); document.write( "the equation determines the value of the dependent variable based on the value of the independent variable.
\n" ); document.write( "x^2 is a function of y meets that definition.
\n" ); document.write( "the value of x^2 is dependent on the value of y.
\n" ); document.write( "the right side of that equation doesn't have to be just y.
\n" ); document.write( "it can be any expression involving y.
\n" ); document.write( "x^2 = y^3 + 5y - 3 would be an example.
\n" ); document.write( "x^2 is a function of y.
\n" ); document.write( "when y = 3, x^3 = 27 + 15 - 3 which becomes:
\n" ); document.write( "x^2 = 39\r
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